Formula omitted] from QCD Laplace sum rule

Abstract

We present a review of our recent works on heavy-light exotic states, with new compact integrated expressions of the spectral functions at lowest order (LO) of perturbative (PT) QCD and up to d=6 condensates of the Operator Product Expansion (OPE). Including higher order (HO) PT corrections, which we have estimated by assuming the factorization of the molecule/four-quark spectral functions, we evaluate masses and couplings with the Laplace sum rules (LSR) and finite energy (FESR) QCD spectral sum rules (QSSR) approaches. Our optimal results based on stability criteria are summarized and compared with experimental candidates and some LO QSSR results. We conclude that, our predicted spectra, do not confirm that the X(5568) is a pure molecule or a four-quark state. The masses of the XZ observed states are compatible with (almost) pure JPC=1+±,0++ molecule or/and four-quark states. The SU3 corrections on the meson masses are tiny: ≤10% (respectively ≤3%) for the c (respectively b)-quark channel but can be large for the couplings (≤20%). We expect that the resonance near the D−K+ threshold can be originated from the 0+(D−K+) molecule and/or D−K+ scattering. The X0(2900), XJ(3150) (if J = 0), X1(2900) and the XJ(3350) (if J = 1) can emerge from a minimal mixing model between tetramoles and first radial excitation. The Zc(3900,4025,4040,4430) and Zcs(3983) spectra are well reproduced by the molecules and tetramoles candidates, or radial excitation.